Finite Group DatabasebetaFinite Group DatabasebetaOrder 37504.
430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×#17989802 | C2 | semidirect |
| 2. #34036450 | C2 | semidirect |
| 3. #34036411 | C2 | semidirect |
| 4. #34036406 | C2 | semidirect |
| 5. #34036326 | C2 | semidirect |
| 6. #34036321 | C2 | semidirect |
| 7. #34036272 | C2 | semidirect |
| 8. #34036239 | C2 | semidirect |
| 9. #34036229 | C2 | semidirect |
| 10. #34036186 | C2 | semidirect |
| 11. #532×C293 | C2 | semidirect |
| 85. Dic586 | #41 | semidirect |
| 87. D1172 | #41 | semidirect |
| 144. C293 | #3115 | semidirect |
| 146. #532 | D293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#17989802 | 2 |
| #34036450 | 2 |
| #34036411 | 2 |
| #34036406 | 2 |
| #34036326 | 2 |
| #34036321 | 2 |
| #34036272 | 2 |
| #34036239 | 2 |
| #34036229 | 2 |
| #34036186 | 2 |
| #532×C293 | 2 |
| #3115 | 293 |